The structure theorem of endomorphism algebras for weak Doi-Hopf modules.
type: Item
instance of: scholarly article
title: The structure theorem of endomorphism algebras for weak Doi-Hopf modules.
zbMATH Open document ID: 1214.16028
author: Ruifang Niu
author: Y. H. Wang
author: Liangyun Zhang
published in: Acta Mathematica Hungarica
publication date: 2011-04-26T00:00:00Z
review text: The paper presents some structure properties of the weak Doi-Hopf modules. Using the condition of weak Hopf-Galois extension, the authors prove the following main result (Theorem 2.8): if \(H\) is a finite dimensional weak Hopf algebra, \(A/B\) is a weak right \(H\)-Galois extension and \(M\) is a weak Doi-Hopf module, then the smash product between the algebra of \(A\)-endomorphisms of \(M\) and \(H^*\) is isomorphic as an algebra with the algebra of \(B\)-endomorphisms of \(M\). By applying this theorem, they obtain the Kreimer-Takeuchi theorem [see \textit{H. F. Kreimer} and \textit{M. Takeuchi}, Indiana Univ. Math. J. 30, 675-692 (1981; Zbl 0451.16005)] and the Nikshych duality theorem for smash products in the case of weak Hopf algebras [see \textit{D. Nikshych}, Contemp. Math. 267, 237-243 (2000; Zbl 0978.16032)].
reviewed by: Mirela Ştefănescu
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 5881186
zbMATH Keywords: weak Galois extensions
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: weak Doi-Hopf modules
zbMATH Keywords: structure theorems
zbMATH Keywords: smash products
MaRDI profile type: Publication
full work available at URL: s10474-010-9134-6
OpenAlex ID: W2149527338
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DOI: 10.1007/S10474-010-9134-6
description: scientific article; zbMATH DE number 5881186